I was going to suggest the Yarra River Trail actually! I think towards Carlton it's the Capital City Trail, and it wasn't until I'd racked up enough k's (and nerve) that I realised you can pretty much follow that trail from North Melbourne, wind along the Yarra via Fairfield and Richmond, and kick on into Fed Square.
Do you just run from near your house, or are you willing to drive somewhere to run? What do you consider difficult; type of road/trail, hills, interruptions like stairs/bridges, stopping for traffic?
I've lived all over the shop, so I've run along a heck of a lot of different paths. If you want a break from the Yarra, try going along the Maribyrnong to Williamtown, or along any stretch of beach like Elwood towards Gardenvale/Brighton, or if you like running in the evening it's pretty quiet cruising around South Melbourne to Docklands.
A quick Google of bike paths got me
here which also links to Bicycle Victoria... I figure if you can ride on it, you can run on it, and other people have already scoped out different places for you to go already.
Otherwise I'd suggest grabbing the Melway for some inspiration. You don't have to go too far into the 'burbs to find a whole heap of parks that have nice scenery, little traffic, and good paths to run on. Have fun. :)